playroom vs game room

playroom and game room both are nouns.

Word	Noun	Adjective	Verb	Adverb
playroom	Yes	No	No	No
game room	Yes	No	No	No

As nouns, playroom and game room are synonyms defined as:

playroom and game room: a recreation room for noisy activities (parties or children's play etc)

Other synonyms of playroom include rumpus room.

playroom (noun)	game room (noun)
a recreation room for noisy activities (parties or children's play etc)	a recreation room for noisy activities (parties or children's play etc)